Does saying, "As for the one who asks, do not repel him," to an Imam who repelled a beggar constitute backbiting, knowing that this is the second time he has done so?

Citing a Quranic verse regarding a ruling, or informing people about an action of an Imam, is not considered backbiting, because it is not something that person would dislike having mentioned about them if they believe in its permissibility. A Muslim should always think well of the Imams and inquire from them respectfully about anything unclear.